A consumer with vN-M utility function U(x) = log(x) and initial wealth W = $500, 000 faces a probability p = 0.2 of incurring a monetary loss of d = $200, 000 in an accident. An insurance company offers him insurance at a price r for each dollar of coverage. That is, if he wants to get back x dollars in case of an accident, he must pay rx dollars for insurance to the company up front. (a) Assume r = 0.25. How much insurance does he buy? (b) Assume now that the insurance company is a monopolist that wants to maximize expected profits. What price would the monopolist charge this consumer? (c) Now suppose the monopolist offers an insurance policy (P, x) to the consumer with x dollars of coverage for a total price of P. What insurance policy will the monopolist choose to maximize
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